Why can't I connect to a wifi network?

I'm trying to connect to a secure WPA2 network on about 6 Windows Phones (all different models). Now, I have data that can not be manually or locally transferred from one phone to the other - it can only be uploaded. So I would definitely need to have internet connection on that device.

4 out of 6 phones connect seamlessly, while the other two return with the message "Can't connect [break] The WiFi network [___] didn't respond. Try again later."

I have verified that the password is correct. I checked, and there is no difference in the fleet's relevant settings, so the working ones are set up identically to the ones that can't connect.